Dynamics of a Predator–Prey System with Impulsive Stocking Prey and Nonlinear Harvesting Predator at Different Moments

Zeli Zhou, Jianjun Jiao (), Xiangjun Dai () and Lin Wu
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Zeli Zhou: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Jianjun Jiao: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Xiangjun Dai: School of Date Science, Tongren University, Tongren 554300, China
Lin Wu: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

Mathematics, 2024, vol. 12, issue 15, 1-21

Abstract: In this article, we study a predator–prey system, which includes impulsive stocking prey and a nonlinear harvesting predator at different moments. Firstly, we derive a sufficient condition of the global asymptotical stability of the predator–extinction periodic solution utilizing the comparison theorem of the impulsive differential equations and the Floquet theory. Secondly, the condition, which is to maintain the permanence of the system, is derived. Finally, some numerical simulations are displayed to examine our theoretical results and research the effect of several important parameters for the investigated system, which shows that the period of the impulse control and impulsive perturbations of the stocking prey and nonlinear harvesting predator have a significant impact on the behavioral dynamics of the system. The results of this paper give a reliable tactical basis for actual biological resource management.

Keywords: predator–prey system; impulsive stocking prey; impulsive nonlinear harvesting; globally asymptotically stable; permanence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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